Prokhorov’s Theorem [1]}: If \(\mathcal {X}\)  is a Polish space, then
a set \(\mathcal {R} \subset \mathcal {P}(\mathcal {X})\)  is pre-compact for the weak topology if and only if it is
tight, i.e. for any \(\epsilon > 0\)  there is a compact set \(K_{\epsilon }\)  such that \(\mu [\mathcal {X} \textbackslash K_{\epsilon }] \le \epsilon \) 
for all \(\mu \in \mathcal {R}\) .
